Spatially variable stage-driven groundwater-surface waterinteraction inferred from time-frequency analysisof distributed temperature sensing data

Kisa Mwakanyamale,1 Lee Slater,1 Frederick Day-Lewis,2 Mehrez Elwaseif,1

and Carole Johnson2

Received 30 December 2011; revised 20 February 2012; accepted 22 February 2012; published 20 March 2012.

[1] Characterization of groundwater-surface water exchangeis essential for improving understanding of contaminant trans-port between aquifers and rivers. Fiber-optic distributed tem-perature sensing (FODTS) provides rich spatiotemporal datasetsfor quantitative and qualitative analysis of groundwater-surface water exchange. We demonstrate how time-frequencyanalysis of FODTS and synchronous river stage time seriesfrom the Columbia River adjacent to the Hanford 300-Area,Richland, Washington, provides spatial information on thestrength of stage-driven exchange of uranium contaminatedgroundwater in response to subsurface heterogeneity. Althoughused in previous studies, the stage-temperature correlationcoefficient proved an unreliable indicator of the stage-drivenforcing on groundwater discharge in the presence of otherfactors influencing river water temperature. In contrast,S-transform analysis of the stage and FODTS data defini-tively identifies the spatial distribution of discharge zonesand provided information on the dominant forcing periods(≥2 d) of the complex dam operations driving stage fluctua-tions and hence groundwater-surface water exchange at the300-Area. Citation: Mwakanyamale, K., L. Slater, F. Day-Lewis, M. Elwaseif, and C. Johnson (2012), Spatially variablestage-driven groundwater-surface water interaction inferred fromtime-frequency analysis of distributed temperature sensing data,Geophys. Res. Lett., 39, L06401, doi:10.1029/2011GL050824.

1. Introduction

[2] The natural contrasts in temperature between ground-water and surface water provide opportunities to use temper-ature to obtain both quantitative and qualitative information ongroundwater-surface water exchange. Groundwater exhibitsrelatively constant temperature compared to surface water,e.g., stream temperatures vary annually on a range between0�C and 25�C [Constantz et al., 1994] whereas groundwatercommonly exceeds the mean annual air temperature of thelocality by 2 to 3 degrees [Bechert and Heckard, 1966] andvaries little over the seasons. The use of fiber optic distributedtemperature sensing (FODTS) allows continuous measure-ments of temperature in both time and space at a high spatio-temporal resolution, and can now be deployed with cablelengths up to thousands of meters, with temperature resolution

of 0.01�C for every meter, and with temporal resolution offractions of a minute. FODTS has been used in a number ofhydrological studies, especially in studies of groundwater-surface water exchange. For example, Selker et al. [2006a]used FODTS in fluvial systems to locate groundwater sour-ces along a stream, whereas Lowry et al. [2007] used FODTSto identify spatial variability in groundwater discharge inwetland systems. FODTS produces rich temporal datasetssuitable for both time series and time-frequency analysis,although, until recently, the benefits of this analysis of FODTSdata have not been fully exploited.[3] The Fourier transform has been used for spectral

analysis of time series for decades. The lack of time loca-lised information in the Fourier spectrum [Mansinha et al.,1997a, 1997b] led to the development of more powerfulmethods that offer joint time-frequency representation oftime series, e.g., the S-transform [Stockwell et al., 1996].Such transforms offer progressive resolution of both timeand frequency. Time-frequency analysis of FODTS datatherefore provides a means to better understand spatial andtemporal variations of hydrological processes by examiningthe frequency content of those processes as a function oftime. Henderson et al. [2009] demonstrated the use of time-frequency analysis of FODTS by using a wavelet transformto characterize the time-variable frequency content of aFODTS temperature time series and comparing it with a tidallevel time series, in order to improve understanding offorcing mechanisms on aquifer-estuary exchange.[4] In this study, we (1) demonstrate the use of time-

frequency analysis to provide proxy indicators of exchangethat are more reliable than parameters extracted from thetime series alone, and (2) obtain spatial information on thestrength of the stage-driven exchange in response to sub-surface heterogeneity along a major river corridor whereheterogeneity is believed to influence the exchange ofUranium contaminated groundwater with river water.

2. Field Site

[5] The 300-Area is located at the south end of theHanford site, north of Richland, Washington (Figure 1a).Uranium contaminated groundwater in the 300-Area dis-charges into the Columbia River through the zone ofgroundwater-surface water exchange along the river corri-dor. The Integrated Field Research Challenge (IFRC) sitehas been established in the 300-Area to study field-scalecontaminant mass transfer processes [Ma et al., 2011]. Ourstudy site is a 1.6-km long portion of the river corridorapproximately centered on the IFRC. The hydrogeologicframework of the river corridor at the 300-Area is defined by

1Department of Earth and Environmental Sciences, Rutgers University,Newark, New Jersey, USA.

2Branch of Geophysics, Office of Groundwater, U.S. GeologicalSurvey, Storrs, Connecticut, USA.

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an upper unconsolidated permeable aquifer (Hanford Forma-tion) overlying a less permeable semi-consolidated and semi-confining unit (Ringold Formation). Geophysical imagingsuggests that the thickness of the Hanford Formation rangesfrom 13.01 to 0.33 m along the 300-Area river corridor, beingthicker towards the north, and thinning out in the south wherethe underlying Ringold Formation is in contact with theriverbed [Slater et al., 2010].[6] The Hanford Formation consists of unconsolidated

sediments, pebble to boulder sized basalts and fine to coarsegrained sand [Kunk and Narbutovskih, 1993] with a highhydraulic conductivity of�2000 m/d [Williams et al., 2007].The Ringold Formation is divided into gravel dominated(upper) and mud dominated (lower) units [Newcomb, 1958].The upper unit consists of cemented and compactedquartzitic gravels with mica rich silt and fine sand matrix[Lindberg and Bond, 1979] with hydraulic conductivity of40–120 m/d [Williams et al., 2007]. The lower unit hashydraulic conductivity of�1 m/d [Williams et al., 2007] andconsists of silty-clay to silty-sand sediments [Tyler, 1992].

Focused exchange between groundwater and river wateralong the Columbia River corridor in the 300-Area isbelieved to be facilitated by buried channels of high per-meability floodwater deposits locally incised below theHanford-Ringold contact during low river stage [Lindbergand Bond, 1979]. These channels are believed to run bothparallel and perpendicular to the river. Slater et al. [2010]found evidence of the paleochannels in waterborne electri-cal imaging surveys and temperature anomalies fromFODTS datasets along the 300-Area river corridor. Theseresults suggest that spatial variation in lithology along theColumbia River corridor is likely to exert a strong controlon stage-driven focused groundwater discharge into theriver. Direct evidence for focused exchange at the riverbedcomes from uranium seeps identified at a number of loca-tions (Spr-7–Spr-11) [Williams et al., 2007] along the rivercorridor (Figure 2). Complex river stage fluctuations

Figure 1. (a) Map of Washington State showing the loca-tion of Hanford Site in Richland, Washington, with the300-Area located in the southeast. (b) Winter temperaturedistribution over 1.6 km of fiber-optic cable placed 2 m fromshore, with the green triangle representing the IFRC well-field area. Temperature measurements at high river stageon 28 February 2009 (line 1). Temperature measurementsat low river stage on 15 March 2009 (80 m offset for clarity)(line 2). (c) Summer temperature distribution over the fiber-optic cable. Temperature measurements at high river stageon 20 August 2009 (line 3). Temperature measurements atlow stage on 3 August 2009 (80 m offset for clarity) (line 4).White dashed circles represent areas of focused groundwater- surface exchange. All color scales are linear.

Figure 2. (a) Temperature distribution time series for aninferred non-exchange area. (b) Temperature distributiontime series for a selected GDZ. (c) Interpolated river stagetime series (black) and the difference in temperature betweenFigures 2b and 2c (blue). (d) Analysis of the completeFODTS cable, with labels at top as follows: temperature dis-tribution for measurements at low stage on 15 March 2009(line 1); correlation coefficient between temperature andriver stage on 15 March 2009 (60 m offset) (line 2); temper-ature distribution for measurements at low stage on 3 August2009 (130 m offset) (line 3); and correlation coefficientbetween temperature and river stage on 3 August 2009(190 m offset) (line 4). White stars represent known uraniumseeps (Spr-7–Spr-11) [Williams et al., 2007]. Red trianglesidentify locations of time series for non-exchange versusexchange locations shown in Figures 2a and 2b, respec-tively. All color scales are linear; the top axis of the colorbar is temperature, the bottom axis displays the correlationcoefficient (CC): JD denotes Julian Day.

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controlled by dam operations upstream of the 300-Area[Lindberg and Bond, 1979] impose a complex flow headboundary condition, regulating groundwater exchange andpresumably influencing uranium transport via these seeps.

3. Methods

3.1. FODTS

[7] The FODTS method is based on measuring the traveltime of a scattered or reflected laser pulse returned frompoints along the fiber optic cable. A portion of the trans-mitted energy is scattered back with wavelength less than(anti-Stokes) and higher than (Stokes) the original wave-length, as a result of (1) density changes in the fiber causedby electromagnetic forces from the passage of light (Bril-louin Scattering) [Selker et al., 2006b], and (2) loss/gain ofenergy exchange with electrons (Raman Scattering) [Selkeret al., 2006b]. The amplitude of the Raman anti-Stokesbackscatter is linearly dependent on temperature. By mea-suring the ratio of the amplitude of the anti-Stokes to theStokes backscatter, temperature can be recorded everywherealong the cable [Selker et al., 2006a, 2006b].

3.2. S-Transform

[8] The S-transform is an extension of the windowedFourier transform that was introduced and defined byStockwell et al. [1996] as a time-frequency representation,whereby the local frequency spectrum is defined at eachpoint along the time axis. This spectral localization is dif-ferent from the wavelet transform [Mansinha et al., 1997a]used to analyze FODTS data by Henderson et al. [2009] inthat the S-transform preserves frequency-dependent resolu-tion while simultaneously maintaining the direct relationshipwith the Fourier spectrum through time-averaging [Stockwellet al., 1996].[9] The 1-D S-transform is based on a moving and scal-

able localizing Gaussian window [Stockwell et al., 1996].The width of this Gaussian window varies as a function offrequency along the time axis as it maps the 1-D time seriesinto a complex function of both time and frequency[Mansinha et al., 1997b]. A complete and lossless invert-ibility between the time (t) to time-frequency (t, f ), tofrequency ( f ) and back to time domain is achieved. The 1-DS-transform is defined as,

S t; fð Þ ¼Z ∞

�∞h tð Þ fj jffiffiffiffiffiffi

2pp e

� t � tð Þ2 f 22 e�i2pftdt ð1Þ

where h(t) is the time series to be analyzed and t is the timeof the spectral localization. Note that the time average ofS(t, f ) gives the Fourier spectrum.[10] The 2-D S-transform provides variations in the

amplitude of a time series for a particular period at eachlocation. The 2-D S-transform is defined using,

S x; y; kx;ky� � ¼

Z ∞

�∞

Z ∞

�∞h x′; y′ð Þ jkxjjkyj

2pe

x′� xð Þ2k2x þ y′� yð Þ2 k2y2

� e�i2p kxx′þ kyy′ð Þdx′dy′ ð2Þ

where x and y are spatial variables and kx and ky are wave-number variables (kx = 1\lx, where lx is the wavelength inthe respective direction).

3.3. Field Data Acquisition

[11] In November 2008, a 1.6 km long ruggedized SensorNetEnviroFlex FO cable (�1 cm diameter) with two 50-micronmultimode fibers was installed on the riverbed at �2 m fromthe river bank, about 0.15 to 0.76 m deep, approximatelycentered on the IFRC area (Figure 1). (Note that any use oftrade, product, or firm names is for descriptive purposes onlyand does not imply endorsement by the U.S. Government).The cable was installed at 2 m from the river bank with theaim of capturing the connectivity between aquifer and theriver. Heavy weights (large cobbles and/or breeze-blocks)were used to anchor the cable to ensure it remained static andunder water. A Sensortran 8-channel Gemini control unit wasprogrammed to collect the water temperature at the river bedevery 0.51 m along the cable (for a total of 2871 measurementlocations) at a 5 min interval. The FODTS system acquireddata continuously for up to 6 mo at a time, with occasionaldown time used for system maintenance and re-calibration. Inthis study, we analyze two uninterrupted parts of the datasetwith lengths of 19 and 30 d acquired during winter and sum-mer months respectively. We are also analyzing the river stagedata collected at 1 hr interval at�1000 m from the IFRC area.

3.4. Time Series and Time-Frequency Analysis

[12] Time series analysis of FODTS data first focused onassessment of the temperature along the cable at different timesof the year to identify likely zones of enhanced groundwater-surface water exchange. Time-series analysis was subsequentlyused to jointly interpret temperature time series and river stagetime series in order to quantitatively evaluate how complexstage variations regulate exchange. Correlation coefficientswere next calculated to evaluate the strength of the lineardependence between temperature and river stage time series forall spatial points along the river corridor.[13] A 1-D S-transform was then used to describe the

frequency content of the temperature signals at selectedlocations along the cable, in order to identify the periodicfeatures present over the time series. Finally, we applied a2-D S-transform to the temperature time series to acquirethe space localized spectral (wavenumber) informationat selected frequencies of interest as identified by the 1-DS-transform [Mansinha et al., 1997b].

4. Results

[14] We first examine temperature variations along thecable at times of low river stage in the time series when thegroundwater discharge into the river is expected to be stron-gest, due to the increase in the groundwater head. Ground-water discharge zones (GDZ) are identified as areas with bothanomalously warm temperature in winter (Figure 1b, line 2)and anomalously cool temperature in the summer (Figure 1c,line 4). Such anomalies are only visible at low river stage(Figures 1b (line 2) and 1c (line 4)) and diminish at high riverstage (Figures 1b (line 1) and 1c (line 3)). The locations of theanomalies are consistent in both winter and summer data.[15] Figure 2 presents the relation between river stage and

temperature for an exchange and a non-exchange zone.These locations are selected for analysis based on theirproximity to the IFRC area and the fact that the zone offocused exchange coincides with a known uranium spring(Spr-9, Figure 2d) [Williams et al., 2007]. The time series inthe non-exchange zone (Figure 2a) shows a temperature

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variation that is primarily driven by diurnal variation. Con-versely, the temperature fluctuation in the GDZ (Figure 2b)shows a diurnal pattern with additional non-diurnal periodsconsistent with what might be inferred from the river stagedata (Figure 2c). As expected, the difference in temperatureis observed in Figure 2c when subtracting the temperature ofthe non-exchange zone from temperature of the exchangezone. The correlation coefficient between river stage andriver water temperature along the cable provides more directevidence of stage-controlled focused groundwater exchangealong the river corridor. The temperature in the focusedGDZ exhibits a weak negative correlation (��0.39 to �0.1)in the winter (Figure 2d, lines 1 and 2) and a strong positivecorrelation (�0.75 to 0.88) in the summer (Figure 2d, lines 3and 4). Outside of the exchange zones, the correlationcoefficient is relatively uniform, �0.48 in the winter and�0.7 in the summer. The sign of the correlation coefficientwithin GDZs is consistent with stage-driven groundwaterdischarge, as discussed below. Although there is a strongcorrelation outside of the GDZs, the sign of the correlation isinconsistent with stage driven groundwater discharge andinstead likely results from stage driven variations in theamount of summer solar heating of the water column.Although the correlation coefficient offers a simple way torepresent the control of stage on focused groundwaterexchange, the relatively weak correlation in the winter data

(Figure 2d, line 2), along with the fact that much of the cable(away from the exchange locations) shows a strong corre-lation in the summer resulting from solar heating (Figure 2d,line 4), raises the need for less ambiguous measures of themechanisms controlling the exchange—hence our consid-eration of the S-transform.[16] Figure 3 shows the 1-D S-transform results of the

river stage time series (Figure 3a), selected GDZ (Figure 3b)and a nearby non-exchange location (Figure 3c) (triangles inFigure 2). Short periods of 0.5 and 1 d characteristic ofdiurnal temperature variations are present in both GDZ andnon-exchange zones. These are the only strong periods in thenon-exchange area. In contrast, the strong amplitudes atlonger periods (2–16 d) in the temperature data from theexchange area correspond well with the strong amplitudesobserved at the same periods in the river stage data(Figures 3a and 3b). These periods are weak (period 7–15 d)or absent (period 2–7 d) in the non-exchange area(Figure 3c). These periodicities are also apparent in the time-averaged normalized power spectra (Fourier Spectrum) plotsshown to the right of the S-transforms in Figure 3.[17] The 2-D S-transform analysis of the entire FODTS

dataset for three dominant periods (4, 1, and 0.5 d) identifiedin Figure 3 is shown in Figures 4b and 4c. The long-periodbehavior dominating the river stage (Figure 3a) is only evi-dent in the zones of focused GDZ (Figure 4b, line 2). Otherlocations along the cable exhibit low amplitudes of ≤0.1 forthe 4-d period. In contrast, the diurnal variations marked byshort periods (0.5 and 1 d) are evident along the entire cablelength (Figure 4c, lines 3 and 4).

5. Discussion

[18] FODTS of riverbed temperature along the ColumbiaRiver reveals the presence of focused groundwater exchangezones which likely facilitate the transfer of uranium from theaquifer to the river. Five identified exchange zones coincidewith known uranium springs reported by Williams et al.[2007]. The relatively similar temperature recorded in theGDZs (�13�C in the winter and �15�C in the summer) isconsistent with groundwater discharge during low riverstage, as groundwater is known to have relatively constanttemperature. The correlation coefficient between tempera-ture and river stage provides a semi-quantitative linkbetween groundwater discharge and river stage at the GDZs.The negative temperature-river stage correlation duringwinter results from discharge of warmer groundwater as theriver stage falls. The positive temperature-river stage corre-lation during summer results from discharge of cooler wateras the river stage falls. However, the high positive correla-tion between temperature and river stage in the non-exchange areas resulting from solar heating or seasonalchanges highlights one limitation of relying on time seriesanalysis of the stage-discharge relation alone for character-izing exchange. Furthermore, there are a few points on thecable where we see negative stage-discharge correlations inboth the winter and summer data (Figure 2d, lines 2 and 4).These responses cannot be due to groundwater-surface waterinteraction.[19] Time-frequency analysis of the FODTS data identi-

fied a distinct difference in the dominant periods of thetemperature time series for the GDZ compared to a non-exchange area. Only diurnal variations in the temperature

Figure 3. S-transform spectrum of time series for 19 d(27 February–16 March 2009). (a) S-transform of the riverstage time series. (b) S-transform of the FODTS time seriesfrom a GDZ. (c) S-transform of the FODTS time series froma non-exchange zone. Plots on the right of the S-transformimages represent the time averaged normalized power spec-tra (equivalent to the FFT), wherein the dashed lines are theriver stage time average for comparison. Color bars displayamplitude (power) linearly.

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time series, marked by short periods of 1 d and 0.5 d appearin both exchange and non-exchange locations. Comparisonof the S-transform for the river stage time series with thetemperature time series shows that long period signals (≥2 d)dominating river stage time series are only present at theGDZ location (Figure 3). We argue that the amplitudes ofthese periods characterizing the stage-time series provide amore reliable indication of active stage-driven groundwaterdischarge relative to analysis of the stage-temperaturecorrelation.[20] The 2-D S-transform computed at these long periods

(e.g., 4 d used here) captures information on spatial vari-ability in the strength of the stage-driven groundwaterdischarge. High amplitudes at these long periods occurat locations along the river corridor (Figure 4b, line 2)corresponding to thicker Hanford Formation deposits(Figure 4a, line 1), possibly associated with buried channelsincised into the Ringold Formation. Figure 4b (line 2) sug-gests that the zones of exchange may be more continuousthan would be inferred using the stage-discharge correlationalone (Figure 2). A thicker Hanford Formation also coin-cides with the location close to the IFRC wellfield exhibitinghigh uranium concentration (Figure 4a) and identified GDZs(Figure 4b, line 2). The known uranium seeps reported byWilliams et al. [2007] (Figures 4a and 4b) all coincide withhigh amplitudes zones in the 4 d period of the temperaturetime series identified with the 2-D S-transform. This is incontrast to the stage-discharge correlation results. Forexample, whereas Spr-8 (Figure 2d) would be interpreted asa non-exchange zone in the stage-discharge correlation plot,the 2-D S-transform identifies Spr-8 as a GDZ (Figures 4a(line 1) and 4b (line 2)). We therefore argue that time-fre-quency analysis provides a more reliable indication of whereexchange is occurring compared to the stage-discharge cor-relation or temperature at low stage alone. The S-transform

analysis suggests that exchange is occurring more continu-ously along sections of the river corridor where the HanfordFormation is thickest. The 1-D S-transform analyses showthat the long period signals related to groundwater-surfacewater exchange have a fairly uniform strength throughout thetime series (unlike the 1 d and 0.5 d periods that are variablein strength). The variation in amplitude in 1 d and 0.5 dperiods from 2-D S-transform analysis in Figure 4c) probablyreflects variations in water depth and effect on solar heating.The time-frequency approach also allows us to effectivelyfilter out all such diurnal effects and focus our interpretationon features in the time series associated with the salientperiodicity of stage.

6. Conclusions

[21] We have demonstrated how the use of time-frequencyanalysis of FODTS time series can provide insights intothe forcing mechanisms controlling groundwater-surfacewater exchange along a major river corridor. The time-frequency analysis using S-transform identified zones ofcontaminated groundwater discharge along a 1.6 km sectionof the Columbia River corridor and provided conclusiveevidence of the stage-driven discharge associated with rela-tively long periods (≥2 d) in the river stage fluctuations. Thecorrelation coefficient between river stage and temperaturealso identified spatial variability in exchange. However,linear correlation proved to be a less robust proxy indicatorof groundwater discharge than the S-transform, as the riverwater temperature and hence correlation responds to vari-ables other than the groundwater discharge alone. We con-clude that time-frequency analysis is a powerful tool forimproving understanding of dynamics of groundwater-sur-face water exchange from the spatially and temporally richFODTS datasets.

Figure 4. (a) Hanford Formation thickness as estimated from continuous waterborne electrical imaging measurements[Slater et al., 2010] (line 1). White stars represent uranium seeps (Spr-7–Spr-11) [Williams et al., 2007]. (b) Amplitude ofperiod 4 d (line 2). (c) Amplitude of period 1 d (line 3) and amplitude of period 0.5 d (60 m offset) (line 4). Long periodsshows strong signals in the exchange zones (thicker Hanford Formation), while we see effect of short periods (≤1 d) for theentire cable length. Brown contours in Figures 4a–4c show uranium concentration (mg/L) [Williams et al., 2007]. All colorscales are linear.

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[22] Acknowledgments. This research was supported by the U.S.Department of Energy under grant DOE - DE - FG02 - 08ER64561 with addi-tional support from the U.S. Geological Survey Toxic Substances HydrologyProgram. We thank Andy Ward, Christopher Strickland, and Jason Green-wood for field assistance. We are also grateful to Roelof Versteeg and Timo-thy Johnson for assistance with data storage and management.[23] The Editor thanks the two anonymous reviewers for their assis-

tance in evaluating this paper.

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